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Mathematical Geosciences

, Volume 42, Issue 3, pp 293–307 | Cite as

Dempster–Shafer Theory Applied to Uncertainty Surrounding Permeability

  • Bree R. MathonEmail author
  • Metin M. Ozbek
  • George F. Pinder
Article

Abstract

Typically, if uncertainty in subsurface parameters is addressed, it is done so using probability theory. Probability theory is capable of only handling one of the two types of uncertainty (aleatory), hence epistemic uncertainty is neglected. Dempster–Shafer evidence theory (DST) is an approach that allows analysis of both epistemic and aleatory uncertainty. In this paper, DST combination rules are used to combine measured field data on permeability, along with the expert opinions of hydrogeologists (subjective information) to examine uncertainty. Dempster’s rule of combination is chosen as the combination rule of choice primarily due to the theoretical development that exists and the simplicity of the data. Since Dempster’s rule does have some criticisms, two other combination rules (Yager’s rule and the Hau–Kashyap method) were examined which attempt to correct the problems that can be encountered using Dempster’s rule. With the particular data sets used here, there was not a clear superior combination rule. Dempster’s rule appears to suffice when the conflict amongst the evidence is low.

Keywords

Evidence theory Groundwater modeling Permeability Dempster’s rule of combination Yager’s rule 

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Copyright information

© International Association for Mathematical Geosciences 2009

Authors and Affiliations

  • Bree R. Mathon
    • 1
    Email author
  • Metin M. Ozbek
    • 2
  • George F. Pinder
    • 1
  1. 1.School of Engineering, Civil & Environmental Engineering ProgramUniversity of VermontBurlingtonUSA
  2. 2.ENVIRON International CorporationPrincetonUSA

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